Units, Scientific Notation, and Significant Figures

Scientific Notation

To make things simpler when expressing very large or small values, scientists express values in terms of "a x 10b", where a is the value and b is number of places the decimal place had to move in order to express a in manageable terms. This type of expression is called scientific notation. Some easy examples of scie ntific notation are provided below.

1 = 1x10⁰
10 = 1x10¹
100 = 1x10²
1000 = 1x10³
and so forth.

The value in the exponent place describes how many zeroes there are in the number being represented. The number 100 has 2 zeroes; it's scientific notation is 1X10² .

In the case of numbers smaller than one, the exponent becomes negative, and that negative value represents how many zeroes there are between the number and the decimal place:

0.1 = 1x10^-1 0.01 = 1x10^-2 0.001 = 1x10^-3

As one can imagine, when expressing extremely large numbers, this method is most helpful. For instance, take the number 602,200,000,000,000,000,000,000. Using scientific notation, this number can be expressed as 6.022x10²3 , which is obviously much more convenient.

Many, many numbers in chemistry, physics, and other sciences will appear in the scientific notation form. It pays to understand it. As we shall see in the next section, scientific notation also is generally more compliant with the rules of significant figures.